In this thesis we study stability from several viewpoints. After covering the practical importance, the rich history and the ever-growing list of manifestations of stability, we study the following. (i) (Statistical identification of stable dynamical syste ...
The goal of fairness in classification is to learn a classifier that does not discriminate against groups of individuals based on sensitive attributes, such as race and gender. One approach to designing fair algorithms is to use relaxations of fairness not ...
Deltas are complex ecogeomorphic systems where features such as channels and interchannel islands are present over a wide range of spatial scales. A quantitative description of the morphology of deltas is fundamental to address how they react to changes in ...
The mechanical coupling between adherent cells and their substrates is a major driver of downstream behavior. This coupling relies on the formation of adhesion sites and actin bundles. How cells generate these elements remains only partly understood. A pot ...
In this thesis, we study several stochastic partial differential equations (SPDE’s) in the spatial domain R, driven by multiplicative space-time white noise. We are interested in how rough and unbounded initial data affect the random field solution and the ...
Environmental transport processes are highly coupled with the shape of landscapes.
Modern catchment analysis with high-resolution data and huge computational powers
demand more detailed within-cell metrics for surface evolution modeling. This
dissertation ...
The Poisson summation formula (PSF) describes the equivalence between the sampling of an analog signal and the periodization of its frequency spectrum. In engineering textbooks, the PSF is usually stated formally without explicit conditions on the signal f ...
We study the nonlinear stochastic heat equation in the spatial domain R, driven by space-time white noise. A central special case is the parabolic Anderson model. The initial condition is taken to be a measure on R, such as the Dirac delta function, but th ...
A numerical method for the solution to the density-dependent incompressible Navier-Stokes equations modeling the flow of N immiscible incompressible liquid phases with a free surface is proposed. It allows to model the flow of an arbitrary number of liquid ...
We propose a simple technique to realize Brillouin slow light in nearly transparent regime. A current-modulated semiconductor laser by a step function is used as Brillouin pump to generate a Brillouin loss doublet. ...
